Wide-range soft anisotropic thermistor with a direct wireless radio frequency interface

Temperature sensors are one of the most fundamental sensors and are found in industrial, environmental, and biomedical applications. The traditional approach of reading the resistive response of Positive Temperature Coefficient thermistors at DC hindered their adoption as wide-range temperature sensors. Here, we present a large-area thermistor, based on a flexible and stretchable short carbon fibre incorporated Polydimethylsiloxane composite, enabled by a radio frequency sensing interface. The radio frequency readout overcomes the decades-old sensing range limit of thermistors. The composite exhibits a resistance sensitivity over 1000 °C−1, while maintaining stability against bending (20,000 cycles) and stretching (1000 cycles). Leveraging its large-area processing, the anisotropic composite is used as a substrate for sub-6 GHz radio frequency components, where the thermistor-based microwave resonators achieve a wide temperature sensing range (30 to 205 °C) compared to reported flexible temperature sensors, and high sensitivity (3.2 MHz/°C) compared to radio frequency temperature sensors. Wireless sensing is demonstrated using a microstrip patch antenna based on a thermistor substrate, and a battery-less radio frequency identification tag. This radio frequency-based sensor readout technique could enable functional materials to be directly integrated in wireless sensing applications.

The bulk "apparent" resistivity values of the four PMC formulations are shown in Supplementary Table 1; these values are calculated assuming the material is isotropic and are therefore distinct form the anisotropic resistivity of the composite, both in-plane and out-of-plane.For the DC response, an increase in the CF loading directly increases the conductivity.On the other hand, the increase in the DC conductivity relates inversely to the stretchability of the material.As observed in Supplementary Table 1, the 40 wt.%CF/PDMS composite has the lowest stretchability, of 40 wt.%, which is due to the stiffness of the CF compared to the PDMS binder.
The maximum TCR is observed in the 20 to 50 o C range for the 30 wt.% CF/PDMS composite, which is due to the trade-off between the room temperature electrical conductivity, increased by increasing the CF loading, and the ability of the expanding polymer matrix (the PDMS) to separate the CFs and increase the observed resistance change.However, based on Supplementary Figure 8 The composite is resilient to cyclic bending and stretching, and has been tested over more cycles (1,000) compared to state-of-the-art soft thermistors, which have only been tested for 200 stretching cycles [36].The effect of simultaneous heating and deformation (both stretching and bending) is presented.
Supplementary Figure 12(a) shows the temperature-resistance relation, for the unstretched pristine thermistor, and under 20.8% strain.As depicted in the diagram, the thermistor is stretched using a clamped fixture and the length between the two measurement electrodes is measured and used to calculate the strain.
The observed shift the in the thermistor's response to higher temperatures is attributed to the compression in the z-axis.The strain increases the room-temperature resistance, in-plane, while decreasing the out-ofplane resistance, as seen in Supplementary Figure 12(b).This causes the sample to exhibit a higher conductivity at higher temperatures, which would otherwise separate all the in-plane contacts between the conductive CFs.
In most wearable applications, however, the components are mostly subjected to bending (which induces compressive and tensile strain [S1]).Supplementary Figure (c) shows that for two bending radii, 1.75 cm and 3.25 cm, the observed change in the thermistor's response is minimal, unlike stretching.Therefore, unless a compensation mechanism is included for independently measuring strain, the sensing functionality of the material is restricted to bendable, but not highly stretchable, applications.This limitation also arises from the stretchability of the RF circuit traces, which might not be implemented using stretchable conductors.
Supplementary From the 0.5-20 GHz measurements, it can be seen that the material's highest sensitivity to temperature is under 5 GHz.This is attributed to the increased dielectric loss in the substrate at higher frequencies.As all sensing resonators are designed for operation under G , the material's broadband relative permittivity and conductivity were measured using a microstrip line up to 6 GHz.The lower measurement frequency was extended to 10 MHz, to approach the low-frequency response of the material; this is limited by the VNA's calibration, to ensure a maximum to minimum frequency ration under 1000:1.
The temperature of the hot plate (setup shown in Supplementary Figure 29) was swept and the temperature over the surface of the thermistor was verified using an infrared camera.The permittivity and conductivity were extracted using supplementary equations ( 4) to (7).Supplementary Figure 20 shows the measured real relative permittivity of the material as well as the conductivity, extracted from the tanδ of the substrate.The logarithmic axes are used to improve the visualisation of the data's trend, due to the non-linear response; the article's full dataset shows the exact data.
/ Supplementary Figure 20.Measured RF properties of the material observed through a 56 mm-long microstrip line.

Figure 12 .
Effect of strain and bending on the composite's resistance: a Measured resistance of the composite over temperature when linearly stretched; (b) room temperature resistance, inplane and out-of-plane, under for various strain values; (c) the measured temperature-resistance relation for different bending radii.

Table 1 .
Summary of the DC and mechanical parameters of the PMCs for different CF/PDMS ratios